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Unit 7, Lesson 4

Comparing Quadratic and Exponential Functions

Algebra 1

Practice

Problem 1

The table shows values of the expressions \(10x^2\) and \(2^x\).

Describe how the values of each expression change as \(x\) increases.
Complete the table.
Make an observation about how the values of the two expressions change as \(x\) becomes greater and greater.

\(x\)	\(10x^2\)	\(2^x\)
1	10	2
2	40	4
3	90	8
4	160	16
8
10
12

Problem 2

Function \(f\) is defined by \(f(x)=1.5^x\). Function \(g\) is defined by \(g(x)=500x^2 + 345x\).

Which function is quadratic? Which one is exponential?
The values of which function will eventually be greater for larger and larger values of \(x\)?

Problem 4

The table shows the values of \(4^x\) and \(100x^2\) for some values of \(x\).

Use the patterns in the table to explain why eventually the values of the exponential expression \(4^x\) will overtake the values of the quadratic expression \(100x^2\).

\(x\)	\(4^x\)	\(100x^2\)
1	4	100
2	16	400
3	64	900
4	256	1600
5	1024	2500

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